Cycle graph

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Explore the main themes, entities and connections around Cycle graph. Start with the topic map, then use the sections below for research and deeper semantic analysis.

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Properties

2-edge colorable 2-regular 2-vertex colorable If and only if Kőnig

18 related topics

Directed cycle graph

Directed graph Feedback arc set Feedback vertex set Cayley graphs Cyclic groups

5 related topics

Terminology

Synonyms Acyclic

2 related topics

Overview

Graph theory Graph Cycle Vertices Simple

9 related topics

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Automorphisms: 2n (Dn)
Chromatic index: 3 if n is odd 2 otherwise
Chromatic number: 3 if n is odd 2 otherwise
Girth: n
Notation: Cn
Properties: 2-regular Vertex-transitive Edge-transitive Unit distance Hamiltonian Eulerian Polytopal

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Graph theory
Graph Graph (discrete mathematics)
Cycle Cycle (graph theory)
Vertices Vertex (graph theory)
Simple Simple graph
Edges Edge (graph theory)
Degree Degree (graph theory)
Loop Loop (graph theory)
Complete graph

Terminology

Synonyms Synonym
Acyclic Directed acyclic graph

Properties

2-edge colorable K-edge colorable
2-regular Regular graph
2-vertex colorable Bipartite graph
If and only if
Kőnig Dénes Kőnig
Connected Connected graph
Eulerian Eulerian graph
Hamiltonian Hamiltonian graph
Unit distance graph
Drawn Graph drawing
Regular polygons Regular polygon
Symmetries Automorphism group
Dihedral group
Symmetric graph
Platonic graphs Platonic graph
Dihedra Dihedron
Dipole graphs Dipole graph
Hosohedra Hosohedron

Directed cycle graph

Sources

Diestel, Reinhard Reinhard Diestel
Springer Springer Science+Business Media
ISBN ISBN (identifier)

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Nodes43

Edges42

Triples25

Avg. degree1.95

Density0.046512

Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Cycle graph

Top relations

related to External links · 6

Cycle graph → Characters, Eric, Expansion, Luca Trevisan, MathWorld, Weisstein

related to Terminology · 4

Cycle graph → Among, The, There, These

related to Properties · 3

Cycle graph → ConnectedEulerianHamiltonianA, Kőnig, More

related to Directed cycle graph · 2

Cycle graph → In, Similarly

see also · 2

Cycle graph → Complete, Null

Automorphisms · 1

Cycle graph → 2n (Dn)

Chromatic index · 1

Cycle graph → 3 if n is odd 2 otherwise

Chromatic number · 1

Cycle graph → 3 if n is odd 2 otherwise

Girth · 1

Cycle graph → n

Notation · 1

Cycle graph → Cn

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

cycle graph vertices graphs number directed cn displaystyle called 2-regular edges least vertex also connected odd simple properties hamiltonian eulerian

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Cycle graph	Automorphisms	2n (Dn)	1.00	infobox
Cycle graph	Chromatic index	3 if n is odd 2 otherwise	1.00	infobox
Cycle graph	Chromatic number	3 if n is odd 2 otherwise	1.00	infobox
Cycle graph	Girth	n	1.00	infobox
Cycle graph	Notation	Cn	1.00	infobox
Cycle graph	Properties	2-regular Vertex-transitive Edge-transitive Unit distance Hamiltonian Eulerian Polytopal	1.00	infobox
Cycle graph	Spectrum	{ 2 cos ⁡ ( 2 k π n ) ; k = 1 , ⋯ , n } {\displaystyle \left\{2\cos \left({\frac {2k\pi }{n}}\right);k=1,\cdots ,n\right\}}	1.00	infobox
Cycle graph	is a	directed version of a cycle graph	0.90	text
Cycle graph	related to Directed cycle graph	In	0.60	section
Cycle graph	related to Directed cycle graph	Similarly	0.60	section
Cycle graph	related to External links	Weisstein	0.60	section
Cycle graph	related to External links	Eric	0.60	section

Related concept clusters Concept neighborhoods

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Connections between topic areas Semantic bridges

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